Magnetic Particle Imaging (abbreviated to “MPI”) is an imaging method which allows the spatial distribution of superparamagnetic nanoparticles (termed magnetic particles here) to be determined, as discussed in [01], for example. This is done by subjecting the magnetic particles in an analysis volume to different static and dynamic magnetic fields and detecting the changes in the magnetization of the magnetic particles using a receiving device. The receiving device is usually equipped with receiving coils for primary signal detection and contains further electronic and/or software components for signal digitization and for analog and digital conditioning and processing of the measurement signals recorded. With MPI, the spatial encoding is undertaken by applying a magnetic gradient field within the analysis volume, which has a field-free region. During an acquisition cycle, the field-free region is shifted along a predefined trajectory (specified course of each point of the field-free region) within the analysis volume with a scanning field (usually a superposition of the gradient field, a dynamic magnetic field (drive field) and/or homogeneous focusing fields). Driving the field-free region across the magnetic particles, and the associated change in magnetization, generates an MPI time signal which is detected by receiving coils. Image data representing the spatial distribution of the magnetic particles can be reconstructed from the MPI time signal.
Conventional MPI reconstruction methods use a discrete Fourier transform to transfer the MPI signal data (MPI time signal) which were recorded in the time domain into the spectral domain block by block. The discrete MPI spectra thus obtained are, however, susceptible to parasitic signals which have a broad spectral distribution due to the so-called leakage effect of the discrete Fourier transform and thus mask the intensity of real signals (useful signals). The MPI time signal recorded is therefore usually a superposition of a useful signal (signal which results from the magnetic particle distribution in the analysis volume) and one or more parasitic signals, e.g. parasitic interferences caused by the object under analysis, from signal transmission, quantization noise, and the like.
With many of the MPI data acquisition and MPI reconstruction techniques known to date, these parasitic signals, including the resulting image interferences, are accepted. A reconstruction is then possible only for comparatively strong useful signals, however. Broadband parasitic interferences may possibly lead to so-called flicker artifacts in the images obtained.
Averaging of several MPI time signals acquired in succession in order to thus reduce the proportion of parasitic signals in the MPI time signal is known from [02]. This leads immediately to a loss of time resolution, however. The number of averagings necessary for a defined damping of those parasitic signals which affect the spectrum via the leakage effect depends on the precise frequency position of the parasitic signal and can possibly be quite large.
Moreover, it is known that parasitic signals can be reduced by using suitable analog or digital filters (high pass, low pass, band stop) [03]. The precise position of the parasitic frequency must, however, be known in order to use filters in a way adapted to this purpose. This is not the case in general. Furthermore, these filters always affect relatively large frequency ranges, and therefore not only the parasitic frequency, but potentially also the useful signal is removed.
The application of window functions is known as an effective way of reducing the leakage effect [04]. A simple windowing leads to a broadening of the frequency spectrum of the individual frequencies (peak broadening), however. This applies to the MPI useful signal too, and thus leads to a mixing of signal components which are actually independent. This means that neither the amplitude accuracy nor the frequency selectivity is guaranteed, which leads to reconstruction artifacts, such that windowing cannot be used without compensation measures. Moreover, there are many different types of window functions which affect the amplitude accuracy, the peak broadening and the reduction of the leakage effect to varying degrees. The selection therefore becomes a difficult compromise.
A further option to reduce parasitic signals is to change the spectral distribution of the parasitic signal by changing the scanning period (period in which the measured values are acquired). With MPI, the minimum scanning period on which a single image is based is predetermined by the duration of an acquisition cycle of the field-free region. This means that, for MPI, an increase in the scanning period can only be achieved by recording of several acquisition cycles. If, however, the discrete Fourier transform is executed over the signal data of several successive cycles, this corresponds to an averaging with the same disadvantage of the loss of temporal resolution discussed above.
Moreover, reference signals which were recorded in a measurement shortly before or after the actual MPI measurement under the same measurement conditions, but without the object under analysis, can be subtracted from the MPI time signals. Apart from the fact that this method leads to a worsening of the signal-to-noise ratio, it is also not suitable to compensate for parasitic interferences which vary in frequency and/or phase from one acquisition cycle to the next, as is the case with the leakage effect.